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. 2013:3:1586.
doi: 10.1038/srep01586.

Systematic breakdown of Amontons' law of friction for an elastic object locally obeying Amontons' law

Michio Otsuki  1 , Hiroshi Matsukawa
Affiliations

Systematic breakdown of Amontons' law of friction for an elastic object locally obeying Amontons' law

Michio Otsuki et al. Sci Rep. 2013.

Abstract

In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law and indicates that the friction coefficient, or the ratio of the friction force to the loading force, is constant. Here, however, using numerical and analytical methods, we show that Amontons' law breaks down systematically under certain conditions for an elastic object experiencing a friction force that locally obeys Amontons' law. The macroscopic static friction coefficient, which corresponds to the onset of bulk sliding of the object, decreases as pressure or system length increases. This decrease results from precursor slips before the onset of bulk sliding, and is consistent with the results of certain previous experiments. The mechanisms for these behaviours are clarified. These results will provide new insight into controlling friction.

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Figures

Figure 1
Figure 1
(a) An elastic object under uniform pressure Pext = FN/(LW) on a rigid substrate is pushed at height h by a rigid rod with shear force FT.(b) The ratio [Image: see text] as a function of [Image: see text]. The horizontal line indicates the value of μM. The inset shows an enlarged view of the box indicated by the red outlines. (c) The local slip region is shown in red in the [Image: see text] plane. The horizontal line indicates the critical length of the quasi-static precursor [Image: see text]. (d) The normalised instantaneous local density of the real contact area in the region of the box indicated by blue outlines in (c). The thin line indicates the position of the precursor front. The results are obtained for [Image: see text], [Image: see text] and parameter set (A).
Figure 2
Figure 2. Macroscopic static friction coefficient μM as a function of [Image: see text] for parameter sets (A) (a) and (B) (b).
The lines with symbols indicate the results of the FEM calculation. Thin lines indicate analytical results based on the 1D effective model, where we set α = 0.2. Lines of the same colour correspond to the same value of [Image: see text].
Figure 3
Figure 3
(a) Macroscopic static friction coefficient μM as a function of [Image: see text] for various values of [Image: see text] and [Image: see text].The open symbols indicate results for the parameter set (A) with [Image: see text] ([Image: see text]), 1.0 ([Image: see text]), and 4.0 ([Image: see text]) and the filled symbols indicate those for (B) with [Image: see text] ([Image: see text]), 0.04 ([Image: see text]), and 0.08 ([Image: see text]). The lines show the theoretical result as obtained with equation (2). The inset shows the [Image: see text] dependence of [Image: see text] for parameter set (A). (b) The normalised pressure [Image: see text] and (c) the ratio of the shear stress to the pressure [Image: see text] at the interface for the magnitudes of [Image: see text] indicated by arrows in Figs. 1(b) and 1(c). The arrows in (c) indicate the positions of the precursor front. The three horizontal lines μS, μM, and μK in order from the top of the panel. The parameters are the same as those for Figs. 1(b–d).
See this image and copyright information in PMC

References

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